In order to reach a fully quantitative ground, ab initio spin dynamics now requires a careful testing of the electronic structure methods underlying it. It is well known that the inclusion of electronic correlation in the simulations is key to achieve accurate prediction of spin Hamiltonian parameters[1]}, [2]}, and the same effect can be expected for spin-phonon coupling coefficients. On the other hand, the simulation of phonon modes requires significant advancements. The introduction of sophisticated vdW corrections to DFT[3]} and the inclusion of anharmonic lattice effects[4]} stand out as two important avenues for future development. The development of efficient simulation strategies is another necessary step towards the widespread use of ab initio spin dynamics. On the one hand, the ab initio methods underlying spin relaxation theory are particularly heavy in computational terms. Magnetic molecules indeed often crystallize in large unit cells and the simulations of phonons beyond the \(\Gamma \) -point is a daunting task. Similarly, the calculation of spin-phonon coupling coefficients requires the quantum chemistry simulations for many similarly distorted molecular geometries, rapidly leading to immense computational overheads. In section  we have hinted to machine learning as a game-changer in this area. Machine learning, learning the underlying features of a distribution from examples drawn out it, makes it possible to interpolate complex functions such as the potential energy surface of a molecular crystal[5]}, [6]} or the relation between spin Hamiltonian and molecular structure[7]}. After the training stage, ML models can be used to make predictions at very little computational cost, therefore offering a significant speed-up of these simulations. Further adaptation of machine learning schemes to this tasks is needed, but encouraging proof-of-concept applications have recently been presented[7]}, [9]}, [6]}, [11]}, [12]}, [13]}. Another interesting strategy involve the use of parametrized Hamiltonians to compute the spin-phonon coupling coefficients. When an accurate parametrization is possible, extensive speed-ups can be achieved[14]}.
